Solitary waves of a PT-symmetric Nonlinear Dirac equation
arXiv:1508.00852 · doi:10.1109/JSTQE.2015.2485607
Abstract
In the present work, we consider a prototypical example of a PT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT-phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the PT-symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the PT-transition threshold. In the latter, they degenerate into linear waves. We also examine the dynamics of the model. Given the stability of the waveforms in the PT-exact phase we consider them as initial conditions for parameters outside of that phase. We find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding "quench". The former can be characterized by an interesting form of bi-frequency solutions that have been predicted on the basis of the SU(1,1) symmetry. Finally, we explore some special, analytically tractable, but not PT-symmetric solutions in the massless limit of the model.
Accepted for publication in the Journal of Selected Topics in Quantum Electronics, special issue on Parity-Time Photonics
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- Soliton dynamics in the ABS nonlinear spinor model with external fields
- Spectral stability of bi-frequency solitary waves in Soler and Dirac--Klein--Gordon models
- Soliton dynamics and stability in the ABS spinor model with a PT-symmetric periodic potential
- Classical Hamiltonian Systems with Balanced loss and gain
- Novel PT-invariant Kink and Pulse Solutions For a Large Number of Real Nonlinear Equations